Potential energy of a system (gravity)

[jjr]

Homework Statement

Show that the potential energy of a system which consists of four equal particles, each with mass M, that are placed in different corners of a square with sides of length d, is given by
e_p = - [itex]\frac{G M^2}{d}[/itex]*(4 + √(2))

Homework Equations

The gravitational force F(r) = - [itex]\frac{G M m}{r^2}[/itex] * u_r
Potential gravitational energy E_p(r) = - [itex]\frac{G M m}{r}[/itex]

The Attempt at a Solution

I'm having a hard time achieveing an intuitive comprehension of how one might solve this problem. As far as I can understand, they're asking how much work would be done if all the particles moved into the center? I'm not sure if I should figure out the work it would take to bring each individual particle into the center one at a time, all at once, or if I need to approach this in some other way.. Any hints would be greatly appreciated

Thanks in advance,
J

 

[ehild]

As far as I can understand, they're asking how much work would be done if all the particles moved into the center?

The gravitational potential is zero at infinity. You need to calculate the work needed to take the system apart, to move the particles one by one to infinity. The negative of that work is equal to the potential energy of the system.


ehild

 

[jjr]

Of course! Thanks:)